Figure 3. Hierarchical prediction of species richness at the scale of 110 km grid cells (N = 9,253).

(A) Conceptual outline of the model and (B) empirical evaluation for the 110 km grid cell Total Richness of Mammals, Birds, and Amphibians. The model first fits differences in grid cell richness among bioregions based on the Resident richness model of bioregion-level diversification (TimeAreaProductivity, Temperature, see Table 1, Figure 2; additional effect of Area was also fitted and significant for Amphibians, see Figure S4, Table S12). Second, the effect of within-bioregion gradients in productivity (CellPropProductivity, i.e., proportion of bioregion grid cell maximum, a measure that standardizes productivity across bioregions) is fitted to predict subsequent sorting of each bioregions' species into grid cell assemblages. The resulting hierarchical prediction of grid cell richness accounts for the scale dependence of different effects and in the case of productivity addresses the different mechanisms of the same variable at different scales. In (B), lines indicate least squares model fits (r ² values for observed–predicted; bioregion level, grid cell level, respectively: r ² [Birds] = 0.40, 0.61; r ² [Mammals] = 0.45, 0.58; r ² [Amphibians] = 0.59, 0.77). Boxplots (left panels) summarize points for each of the 32 bioregions. Colors indicate biome membership (see Figure 2 for legend). See also Figure S4 and Tables S12 and S13. Partial residuals illustrate the relationship between a predictor and the response given other predictors in the model.